보다 - To see/look/watch 지역 - local I watched a movie at the local movie theater - (나는) 지역 극장에서 영화(를) 봤어요 I hope my explanation will be helpful :)

"I watched a movie at the local movie theater." (나는/저는) 집 근처 / 동네 극장에서 영화를 봤어요.(formal) 집 근처 / 동네 극장에서 영화를 봤어. (informal) "Local" literally means "지역" in Korean, but I think in the context of your sentence. 집 근처 (near to my house), or 동네 (my neighborhood) will be better. Also I would like to introduce some vocabulary and expression. 영화관/극장 movie theater 극장 theater for a play or a concert 경기장 stadium or arena for sport event 관객 moviegoer, movie spectator/audience or audience at performances such as a play or a ballet. 시청자 television viewer 청취자 radio listener 관중 spectators at sports events 영화 보러 가다 go to theater

"보다" is the most general translation of the English verbs "see", "look", and "watch". "극장에서 영화 봤어요" sounds very natural. You did a good job.